A conventional photodiode converts an incident photon into a photocurrent by exploiting material properties of a semiconductor. A semiconductor has an energy band structure with a band gap between a pair of adjacent energy levels as shown in FIG. 1, where E is band energy and k representing kx, ky, kz is the transverse momentum. The conduction and valence bands have quadratic dispersion as indicated by their quadratic curvatures.
A semiconductor absorbs incident photons whose energy matches the band gap energy. Each absorption creates an electron-hole pair in the semiconductor. Applying a voltage to the semiconductor causes the electrons and holes to propagate in opposite directions, creating a photocurrent whose amplitude is proportional to the number of photons absorbed per second by the semiconductor.
Not every material has an energy band structure with gaps between adjacent energy levels. Graphene, for example, has energy band structure with bands that touch each other at different points in momentum space as shown in FIG. 2. These intersection points are called Dirac points or Dirac vertices. They represent degeneracies between two energy bands with linear dispersion, which can be characterized as a linear change in energy E with spatial frequency kx, ky, or kz. When viewed from one direction (e.g., the x, y, or z direction), a Dirac point appears at the intersection between the linear portions of the energy bands.
Electronic materials with band crossing excitations have recently attracted much interest in condensed matter physics. A two-dimensional (2D) Dirac spectrum describes the surface states of three-dimensional (3D) topological insulators and also the bulk excitations of graphene. Their gapless and topological characters have stimulated many electronic applications, one of which is the photovoltaic effect. The linearly crossing dispersions of Dirac systems can absorb photons with, ideally, arbitrarily long wavelength, making them possibly advantageous for infrared (IR) detections. Nevertheless, the generation of photocurrent from transitions between the topological surface states, defined as the spontaneous production of current without any applied voltage in response to exposure to light, vanishes for an ideal Dirac spectrum in 2D because of the symmetric excitations about the Dirac point. In fact, the resultant photocurrent may be negligible even if realistic perturbations including band curvatures, warpings, and Zeeman couplings are taken into account. To date, the generation of a substantial photocurrent in Dirac systems has involved either using high frequency light to produce a small effect due to the transition between bulk and surface states in topological insulators or external assistance, such as a theoretical proposal of coupling to a magnetic superlattice. (Similarly, quantum wires require external magnetic fields to create sizeable photocurrents.)